Property (T) of Groups, Groupoids, and C*-algebras and their relationships

Bekka has defined a notion of property (T) for C-algebras that is congruous with property (T) groups in the sense that any C-completion of the complex group ring has property (T) if and only if the group does. We will outline the fairly straightforward proof of this fact, as well as discuss some ideas that Joav Orovitz and I have for ”generalizing“ property (T) for C*-algebras so that the analogous statement is true for groupoids and completions of their convolution algebras.